Synthesis of mechanisms using homotopy methods including considerations of rotatability, circuit defect and branch defect

The research presented in this dissertation concerns, circuit defect, branch defect and rotatability of input links in design of planar and spatial mechanisms. General theoretical frameworks are developed for mechanisms with these properties with two closures and a quadratic input-output equation as well as four closures and a quartic input-output equation.; For mechanism with two closures, identifiers are provided for circuit defect and branch defect, and an analytical method is developed for synthesizing linkages with quadratic input-output equation which are free from circuit and branch defect. In addition, it may be required to have full rotatable cranks. A novel concept called the range defect of the input link is introduced. It is shown that the range defect results in a circuit defect. Further, all circuit defects except those introduced as a result of range defects can be eliminated by eliminating branch defects. The circuit defect introduced by the range defect is eliminated by first eliminating the range defect and then eliminating the branch defect. It is also shown that the notions of assemblability, rotatability, circuits, branches, and locking positions are different for mechanisms with four closures compared to mechanisms with two closures. Assemblability, rotatability of input cranks are branch independent properties for mechanisms with two closures, whereas for mechanisms with four closures the input link rotatability are not only branch dependent but also starting position and direction of motion dependent.; Homotopy method with m-homogenization are used to get all complete solutions to precision position type function, motion and path generation synthesis problems of slider-crank, four link, Watt six link, and Stephenson six link mechanisms with varying number of specified precision positions.; The general theory of mechanism design for determining conditions for assemblability, rotatability of input crank, locking positions, multiplicity of circuits and branching of mechanism with two closures and four closures, and complete solutions using homotopy method with m-homogenization for synthesis problems are the original contribution of this work.